The most common problems i have observed in LN are
1. Compatibility issue as theymos stated earlier, when we have an up gradation there are always some compatibility issues, although it can be eliminated with time but still it is one of the major issues.
Second, LN often does not integrate easily with existing BTC payment systems. For example, I would have to almost completely rewrite the bitcointalk.org payments system in order to make it work with LN. (Someday I'll do it, but not soon.)
2. Limitation of funds transfer through channels, unfortunately LN will not support big/bulky transactions, you have to rely on your active channels and their capacity.